On some pointwise inequalities involving nonlocal operators

TL;DR

This paper surveys known pointwise identities involving fractional operators, introduces a unified approach to these identities, and proves new identities across various frameworks including geometric and infinite-dimensional settings.

Contribution

It provides a comprehensive survey, a unified method, and new pointwise identities for nonlocal fractional operators across different mathematical frameworks.

Findings

Unified approach to pointwise identities

New identities in geometric frameworks

Extension to infinite-dimensional settings

Abstract

The purpose of this paper is three-fold: first, we survey on several known pointwise identities involving fractional operators; second, we propose a unified way to deal with those identities; third, we prove some new pointwise identities in different frameworks in particular geometric and infinite-dimensional ones.